Cement slab touches buildings

The original cement slab was poured about 2 inches from the bottom of the door jam, so the cement actually covers the siding. The 2 adjacent homes are basically connected with the slab. The slabs have moved and there are puddles everytime it rains. We have caulked along side the slab onto the house because some of the siding has gotten wet. This sort of works, looks tacky and could be improved. I just don't know how it could be improved.
One person said to remove some of the cement. Re-pour a new 4" slab and make it so that the water drains to the middle. Is there a better way to redo this whole slab touching-the-siding problem? One end of the slab may be 9" thick and the other end is 9" thick but sits on the cement steps. The slab actually is the top for the steps. Would it be better to remove all cement and use composite decking material? Any suggestions would be great. Thank you.